The alignment of clusters of galaxies with their nearest neighbours and bet
ween clusters within a supercluster is investigated using simulations of 51
2(3) dark matter particles for Lambda CDM and tau CDM cosmological models.
Strongly significant alignments are found for separations of up to 15 h(-1)
Mpc in both cosmologies, but for the Lambda CDM model the alignments exten
d up to separations of 30 h(-1) Mpc. The effect is strongest for nearest ne
ighbours, but is not significant enough to be useful as an observational di
scriminant between cosmologies. As a check of whether this difference in al
ignments is present in other cosmologies, smaller simulations with 256(3) p
articles are investigated for four different cosmological models. Because o
f poor number statistics, only the standard CDM model shows indications of
having different alignments from the other models.